1.6 Complement

Class: CSE 16 Subject: computer-science discrete-math Date: 2024-10-02 Teacher: Prof. Musacchio

Sets

Complement

Universal Set

• it refers to the set that some set $A$ that contains all the elements of $A$
  • E.g. Prime numbers, $\mathbb{P}$ = { 2,3,5,7,11,13,… } $\subseteq$ $\mathbb{N}$ with $\mathbb{N}$ being the universal set

Complement Def

• Let $A$ be a set with a universal set $U$. The complement of $A$ denoted $\overline{A}$, is the set $\overline{A}$= $U$ − $A$.
  • $\overline{A}$ = {x: x $\in$ $U$ - $A$}

Examples

• If $P$ is the set of prime numbers, then,
  • $\overline{P}$ = $\mathbb{N}$− $P$ = { 1, 4, 6, 8, 9, 10, 12,… }

Order of Operations

1. complements
2. intersections
3. unions
4. differences

Examples

$\overline{A\cap B}=\overline{A}\cup \overline{B}$